Ordinary differential equations

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Title:

Personal Author:

Greenberg, Michael D.

Publication Information:

Hoboken, N.J. : Wiley, 2012

Physical Description:

xviii, 526 p. : ill. ; 26 cm.

ISBN:

9781118230022

Abstract:

"After a brief review of first-order differential equations, this book focuses on second-order equations with constant coefficients that derive their general solution using only results described previously. Higher-order equations are provided since the patterns are more readily grasped by students. Stability and fourth order equations are also discussed since these topics typically appear in further study for engineering and science majors. In addition to applications to engineering systems, applications from the biological and life sciences are emphasized. Ecology and population dynamics are featured since they involve both linear and nonlinear equations, and these topics form one application thread that weaves through the chapters. Diffusion of material, heat, and mechanical and electrical oscillators are also important in biological and engineering systems and are discussed throughout. A complete Instructor Solution Manual is available upon request and contains solutions to all exercises as well as Maple[trademark symbol] code. While the book is not dependent on the use of one specific software, some of the exercises do call on the use of such systems to solve certain differential equations or to plot the results. A Student Solutions Manual is available to supplement the book, and while the first manual will feature Maple, the author is also preparing versions using Mathematica and MATLAB;to accommodate instructor preferences. Chapter coverage includes First-Order Differential Equations; Higher-Order Linear Equations; Applications of Higher-Order Linear Equations; Systems of Linear Differential Equations; Laplace Transform; Series Solution; Systems of Nonlinear Differential Equations; and Appendices on Partial Fraction Expansions, Determinants, Gauss Elimination, and Complex Numbers and the Complex Plane"

Subject Term:

Differential equations -- Textbooks

Differential equations, Partial -- Textbooks

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010293736	QA372 G74 2012	Open Access Book	Book	Searching... Unknown

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Summary

Features a balance between theory, proofs, and examples and provides applications across diverse fields of study

Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory.

Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps and provides all the necessary details. Topical coverage includes:

First-Order Differential Equations

Higher-Order Linear Equations

Applications of Higher-Order Linear Equations

Systems of Linear Differential Equations

Laplace Transform

Series Solutions

Systems of Nonlinear Differential Equations

In addition to plentiful exercises and examples throughout, each chapter concludes with a summary that outlines key concepts and techniques. The book's design allows readers to interact with the content, while hints, cautions, and emphasis are uniquely featured in the margins to further help and engage readers.

Written in an accessible style that includes all needed details and steps, Ordinary Differential Equations is an excellent book for courses on the topic at the upper-undergraduate level. The book also serves as a valuable resource for professionals in the fields of engineering, physics, and mathematics who utilize differential equations in their everyday work.

An Instructors Manual is available upon request. Email sfriedman@wiley.com for information. There is also a Solutions Manual available. The ISBN is 9781118398999.

Author Notes

MICHAEL D. GREENBERG, PhD , is Professor Emeritus of Mechanical Engineering at the University of Delaware where he teaches courses on engineering mathematics and is a three-time recipient of the University of Delaware Excellence in Teaching Award. Greenberg's research has emphasized vortex methods in aerodynamics and hydrodynamics.

Preface	p. viii
1 First-Order Differential Equations	p. 1
1.1 Motivation and Overview	p. 1
1.2 Linear First-Order Equations	p. 11
1.3 Applications of Linear First-Order Equations	p. 24
1.4 Nonlinear First-Order Equations That Are Separable	p. 43
1.5 Existence and Uniqueness	p. 50
1.6 Applications of Nonlinear First-Order Equations	p. 59
1.7 Exact Equations and Equations That Can Be Made Exact	p. 71
1.8 Solution by Substitution	p. 81
1.9 Numerical Solution by EulerÆs Method	p. 87
2 Higher-Order Linear Equations	p. 99
2.1 Linear Differential Equations of Second Order	p. 99
2.2 Constant-Coefficient Equations	p. 103
2.3 Complex Roots	p. 113
2.4 Linear Independence; Existence, Uniqueness, General Solution	p. 118
2.5 Reduction of Order	p. 128
2.6 Cauchy-Euler Equations	p. 134
2.7 The General Theory for Higher-Order Equations	p. 142
2.8 Nonhomogeneous Equations	p. 149
2.9 Particular Solution by Undetermined Coefficients	p. 155
2.10 Particular Solution by Variation of Parameters	p. 163
3 Applications of Higher-Order Equations	p. 173
3.1 Introduction	p. 173
3.2 Linear Harmonic Oscillator; Free Oscillation	p. 174
3.3 Free Oscillation with Damping	p. 186
3.4 Forced Oscillation	p. 193
3.5 Steady-State Diffusion; A Boundary Value Problem	p. 202
3.6 Introduction to the Eigenvalue Problem; Column Buckling	p. 211
4 Systems of Linear Differential Equations	p. 219
4.1 Introduction, and Solution by Elimination	p. 219
4.2 Application to Coupled Oscillators	p. 230
4.3 N-Space and Matrices	p. 238
4.4 Linear Dependence and Independence of Vectors	p. 247
4.5 Existence, Uniqueness, and General Solution	p. 253
4.6 Matrix Eigenvalue Problem	p. 261
4.7 Homogeneous Systems with Constant Coefficients	p. 270
4.8 Dot Product and Additional Matrix Algebra	p. 283
4.9 Explicit Solution of xÆ = Ax and the Matrix Exponential Function	p. 297
Nonhomogeneous Systems	p. 307
Laplace Transform	p. 317
Introduction	p. 317
The Transform and Its Inverse	p. 319
Applications to the Solution of Differential Equations	p. 334
Discontinuous Forcing Functions; Heaviside Step Function	p. 347
Convolution	p. 358
Impulsive Forcing Functions; Dirac Delta Function	p. 366
Series Solutions	p. 379
Introduction	p. 379
Power Series and Taylor Series	p. 380
Power Series Solution About a Regular Point	p. 387
Legendre and Bessel Equations	p. 395
The Method of Frobenius	p. 408
Systems of Nonlinear Differential Equations	p. 423
Introduction	p. 423
The Phase Plane	p. 424
Linear Systems	p. 435
Nonlinear Systems	p. 447
Limit Cycles	p. 463
Numerical Solution of Systems by EulerÆs Method	p. 468
Review of Partial Fraction Expansions	p. 479
Review of Determinants	p. 483
Review of Gauss Elimination	p. 491
Review of Complex Numbers and the Complex Plane	p. 497

Available:*

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Summary

Summary

Author Notes

Table of Contents